When chatting with a new acquaintance for a few minutes, our profession often comes into the conversation and then takes over. We're all familiar with this line at grocery stores, airplanes, trains, and more.

MATH? Oh, I was never a math person.

The conversation then continues on a predictable trajectory. The interesting thing I have noticed is: during conversations like this, our new acquaintance is actually willing to consider our opinion. There is usually time to give them about one new sentence about mathematics or mathematics education to think about. This means these conversations are actually a unique educational opportunity.

This leads to my question: When you have a willing audience of one, and you are able to transmit exactly one idea about mathematics or mathematics education, what do you choose?

Note my goal is not to steer the conversation away from math; they want to talk about it and want to listen a tiny bit. How can we make this an effective learning experience?

There was an MO question that resembles this one a bit mathoverflow.net/questions/5353/…, but it was more open and most of the answers given there (at least from the topvoted one, I did not check all) would not apply here as they do often not focus on conveying something about math.
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quid♦May 19 '14 at 15:29

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RE one idea. That most people think in a way that involves some sort of mathematics in their daily lives, and that the word "mathematics" - whatever it means - is not the same as arithmetic, school math, or test math.
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Benjamin DickmanMay 19 '14 at 22:23

Actually, this reaction is not that common. Just today I was telling an art historian that I am a mathematician and he asked if I liked the Sokal hoax. Then we were discussing the relative difficulty of doing art history and mathematics in a foreign language.
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user11235May 20 '14 at 23:26

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For people with a bad math experience that I do not know well, it is quite satisfactory to convey that I really love mathematics, that this positive feeling is about ideas, seeing a pattern and then proving that the pattern is true. I really think that this talk about applications in daily life is a red herring. So yes, mathematics can be useful, but that is really no reason to like it.
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user11235May 20 '14 at 23:32

6 Answers
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I used to be "not a math person" as well, but I stuck with it, and eventually I learned what math was all about and I fell in love.

My response may make me seem like a bit creepy -- after all who "falls in love" with math but creepy people? -- but it has the benefit of inviting follow-up questions that are positive in nature. "Oh really? Did you have a good teacher? What is math all about anyway?"

It also has the benefit of being true. Math was my worst subject, by far, in school until my senior year of high school, when I had a teacher who gave me the time and space in class to explore Calculus on my own. Later still in college, the light bulb went off for me when I was taking abstract algebra and I learned about isomorphisms and it all just came together for me.

So what I'm saying here is that I'd communicate the idea that "not math people" can become math people given the right combination of instruction, persistence, and inspiration -- and that a person can have a deeply personal relationship with this subject given the chance.

This happened to me two days ago! The "What is it that you teach then?" conversation.

I first said everyone's different and has different brains, and that a bunch of us who did PhDs together decided being a PhD mathematician was a mild form of mental disease, with a lot of common symptoms (that I won't need to list to anyone who's spent a lot of time observing people who teach postgraduate mathematics), and told her to ask my wife about my maths friends at our wedding, remembered by the families for ever.

The wall

I explained we all hit a wall in maths at some stage, (the wall being where your innate talent becomes insufficient to get on without a significant increase in effort, reached at very different ages by different people).

With a good teacher, you learn to climb over the wall and start finding wall climbing enjoyable. If the teacher at the time doesn't get you over your personal wall, then because it's so hierarchical (I didn't use that word) and jargon-laden, it's easy to get left behind and conclude maths is impossible and leave demoralised. I went on to explain how I've managed to get my students this year much better at (metaphorical) wall climbing, and they're the best bunch in terms of mock exam results I've had for a long long time.

She went on to tell me about her personal wall at work (tracheotomy re-insertions) and decided she wanted to do something about it - planning to start observing her colleague doing it and get accredited to do it. Apparently she's felt for more than a decade she ought to be able to do this, but decided to actually do something about it when hearing that it's possible for students who find mathematics hard to get past that! I don't know whether she'll follow through on that, but I'm delighted that some of what I said must have meant something to her.

This suggests the question: How should we teach mathematicians the proper etiquette for non-mathematical situations? I might ask just so you can answer with the story about the wedding.
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Matt F.May 19 '14 at 17:04

Agreed with Matt F., OP needs to deliver on the wedding story. :)
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Robert TalbertMay 19 '14 at 20:50

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It's just that if you take a mathematician and put them in a room with other people, they sometimes stand out a bit. PhD maths students stand out a little in a room of undergraduates. If you take six PhD maths students, including one who stands out amongst PhD maths students as rather odd, you have a bunch of people who really stand out amongst everyday folk. Everyone says they were nice, but certainly extraordinary. On the whole my in-laws seem pleased that I turned out as near-regular as I did. I don't tell them I answer questions for fun on the internet and use spreadsheets recreationally.
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AndrewCMay 19 '14 at 21:00

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To make an analogy to explain why the families see this as a big deal; imagine you never met or saw anyone who wore a cape and then six people with capes spent two days with you, and the fact that there were six of them meant the capes came out, followed by you never seeing any more capes for the rest of your life because you only ever saw them one or two at a time. You might talk about the six caped men for decades to come. The Maths PhD community saw life through a rather unique perspective, which, incidentally, made it fabulous to be in, and these friends of mine are fabulous people.
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AndrewCMay 19 '14 at 21:19

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Isaac Asimov wrote about hitting his "wall" in mathematics (at integral calculus) in his book Opus 100 (pp. 89-90). I posted the entire excerpt in this 8 March 2010 math-teach post at Math Forum. By the way, my comments -- Any bets on how long after I post this before it starts to show up on people's blogs and web sites? My guess is 2 to 3 months -- seem to have been overly optimistic.
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Dave L RenfroMay 21 '14 at 15:35

Here in the US, kids usually get their first instruction in math (aside from learning to count) in public schools, from teachers with multiple-subject credentials. Some of these folks are wonderful at teaching math, but many of them limped through their own math coursework without understanding it very well, and hated math themselves. If a kid goes through 1st through 5th grades and has four teachers who are fantastic at teaching math and one who is terrible, often that kid ends up hating math. All it takes is a bad experience during one year, and the kid generalizes: I can't do math past this level because I'm not smart enough, and math past this level is too hard and scary and doesn't connect to real life.

at the grocery store: Did your teachers ever talk with you about fitting
oranges in a box? And how every orange ends up touching 12 others?

at the bus stop: Did you ever watch a single point on a bus tire,
to see its path as the bus moves? It looks like this (draw a cycloid in the air),
and the curve turned out to be useful for clock-makers.

I'm glad I liked it and learned it well.
I got 20 years of jobs based on my mathematical skills.

Then I can talk about math in whichever job seems right for the context. That might be health care, defense, academia, software, finance, consulting....I would emphasize that math has opened a lot of doors for me.

I have yet to find the solution for this problem which works for myself. However, I heard a great story at a donut shop in Brooklyn a few years ago. I think this works for a bus stop or train station, whatever. This was told to a youngster by an elderly gentleman who was enjoying some conversation about pop culture whilst the the youngster and his friends were rather rowdy. First, he did not judge the boy. Second, he just started talking to him. I'll recount the story briefly: